Simplify the following expression: $r = \dfrac{8k^2 - 96k + 216}{k - 9} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $8$ , so we can rewrite the expression: $ r =\dfrac{8(k^2 - 12k + 27)}{k - 9} $ Then we factor the remaining polynomial: $k^2 {-12}k + {27} $ ${-9} {-3} = {-12}$ ${-9} \times {-3} = {27}$ $ (k {-9}) (k {-3}) $ This gives us a factored expression: $\dfrac{8(k {-9}) (k {-3})}{k - 9}$ We can divide the numerator and denominator by $(k + 9)$ on condition that $k \neq 9$ Therefore $r = 8(k - 3); k \neq 9$